Question

You have a coupon for your favorite clothing store for $25 off any purchase of more than $50. The store is also running a 20%-off sale on its entire inventory. Let x be the original price, f(x) be the price with the $25 coupon applied, and g(x) be the price with the 20% discount applied.

a. Write an expression for f(x).

b. Write an expression for g(x).

c. What would the expression (f o g)(x) represent?

d. What would the expression (g o f)(x) represent?

e. If the store allows you to apply both the 20% discount and the $25-off coupon, does it matter which you apply first? How do y

Answer 1

f(x) = (1 - 0.25)x = 0.75x
f(x) = 0.75x

g(x) = (1 - 0.2)x = 0.8x
g(x) = 0.8x

(f o g)(x) = f(g(x)) = 0.75(0.8x) = 0.6x
(f o g)(x) = 0.6x

(g o f)(x) = 0.8(0.75x) = 0.6x
(g o f)(x) = 0.6x

It does not matter which one you apply first.